The assignee of the present invention has for a number of years marketed high speed rotary handpieces, for example under the model designation 100 K, and more recently 100 K2 (a 100,000 rpm handpiece). While these prior art handpieces (which include prior art chucks), and chuckable tools to be used therewith, have worked well and been commercially successful, the present invention was developed in a continuing effort to improve on apparatus of this general type.